https://en.m.wikipedia.org/wiki/Azeotropic_distillationYou can't distill ethanol to 100%, only 95%. To get the last 5% of water out you typically add benzene or cyclohexane, which remains as a trace contaminant in the final product.
Also note that methanol (and other unsavory small molecules) normally contaminate distilled ethanol unless you actively take steps to remove them. For something you intend to drink, you need to carefully control fermentation to reduce the amount of methanol, toss out the early distillation fractions to remove as much methanol as you can, and then let your remaining distillate sit in an open tank for a couple of weeks to let whatever methanol remains evaporate off (along with some of your product).
If you're making ethanol as an industrial solvent or fuel, you don't need to do these things. It's not crazy that under prohibition, taking all those extra steps would be seen as evidence of an intention to violate the law and make drinkable spirits.
But whatever, Slate says it was a conspiracy to poison poor people, I'm sure that's the right explanation.